What are the characteristics of the
exponential distribution?
In reliability engineering the exponential distribution
has been found to adequately model the failure rate of electronics during their
useful life [1]. The probability density function (PDF) for the exponential
distribution is shown in Figure 1 and is given below by Equation 1. For any time
period of interest, t, the area under the PDF curve from t to infinity is equal
to the reliability, R(t). The area under the PDF curve to the left of t is equal
to the probability of failure (1R(t)).
f(t)=le^{}^{lt
}[
1 ]
The cumulative distribution function
(area under PDF curve) is obtained by integrating the PDF as shown in Figure
2 and given by Equation 2.
_{
}
[ 2
]
Figure
1  Probability Density Function (Exponential Distribution)
Figure
2  Cumulative Distribution Function
The reliability
function (probability that a device will not fail), is given by Equation 3.
R(t)=1F(t)== e^{lt}
[ 3 ]
Figure
3  Reliability
Function (Exponential Distribution)
The hazard function is given by Equation
4. For the exponential distribution, the hazard function, or instantaneous
failure rate, is constant over time, as shown in Figure
4. This is one of the fundamental relationships of reliability analysis
and allows for the simple addition of component failure rates to obtain
equipment or system level failure rates. It is a measure of the change in
survivor rate per unit time.
_{
}
[ 4 ]
Figure 4
 Hazard Function (Exponential Distribution)
[1]
MILHDBK338, Electronic Reliability
Design Handbook, 15 Oct 84.
